This program computes all possible alphanumeric passwords of 

length three, and it uses that list to crack a fake password

that's stored in a separate file.

​

Only basic JS is used so that new programmers

can understand the code.

*/

​

​

// manually guess the password

// authenticate(password) returns true if correct, false if not

// note: the authenticator is defined in a separate file

​

console.log(authenticate('2fX'));

​

// now let's try to crack the password

// start by making an array of the possible characters

// and build all possible passwords (of length 3) from that

​

const CHARACTERS = [

  'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 

  'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z',

  'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 

  'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z',

  '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'

];

​

// cartesianStrings(array1, array2)

// returns Cartesian product of two arrays of strings

// array1 = [x1, ... , xm] and array2 = [y1, ..., yn],

// with the ordered pair ('x','y') represented as 'xy' (for example)

​

/*

Note: with modern built-in JS functions, it's 

possible to compute the Cartesian product of arbitrarily 

many arrays in just one line of code. See 

​

https://stackoverflow.com/questions/12303989/cartesian-product-of-multiple-arrays-in-javascript

​

In the solution given there, n-tuples are represented as arrays

of length n, so it would need to be modified to return passwords

of length n as strings.

*/

​

function cartesianStrings(array1, array2) {

  let product = [];

  for (let i = 0; i < array1.length; i++) {

    for (let j = 0; j < array2.length; j++) {

      product.push(array1[i]+array2[j]);

    }

  }

  return product;

}

​

const PASSWORDS = cartesianStrings(cartesianStrings(CHARACTERS, CHARACTERS), CHARACTERS);

​

// check that we have 62 ** 3 = 238328 passwords

console.log(PASSWORDS.length);

​

// use our list to crack the password!

for (let i = 0; i < PASSWORDS.length; i++) {

  if (authenticate(PASSWORDS[i])) {

    console.log(`Password: ${PASSWORDS[i]}`);

    break;

  }

}

​

// you can check authenticator.js to see if you got it correct :)